A Juan Fernández firecrown hummingbird, found only on the Juan Fernández islands. Photograph: John Francis/CORBIS

The unique wildlife of the island that inspired Robinson Crusoe is teetering on the edge of annihilation, according to the Chilean government, which has launched a last-ditch attempt to save it.

The Juan Fernández islands lie 600km out into the Pacific ocean and host an extraordinary number of unique plants and animals which occur nowhere else in the world. The threat comes from alien invaders, including rats, goats and even brambles.

"This is a key challenge for Chile," says Miguel Stutzin Schottlander, head of the Chilean government's Department for the Protection of Natural Resources. "This is a starting point, bringing together stakeholders from civil society and the scientific community to set priorities. We are dealing with the threat of extinction of an important part of our heritage and it's a big responsibility."

"This is one of the global jewels of biodiversity," says Peter Hodum, an ecologist from the University of Puget Sound, US, who leads the conservation organisation Oikonos, "Although it does not have the cache of the Galápagos, it is just as important."

The Juan Fernández islands include the island on which the castaway Alexander Selkirk spent four lonely years. His story became Daniel Defoe's Robinson Crusoe, after whom the island is now named.

From the windy look-out from where Selkirk scanned the horizon for ships, conservationists dream of rescue too. "The important thing about this biodiversity is that it has a meaning for itself, but it's up to us to take care of it," says Ivan Julio Leiva Silva who, as director of the Juan Fernández national park, has been struggling with its problems for 15 years.

The Juan Fernández firecrown – a tiny, ginger hummingbird found solely on Robinson Crusoe island, and one of the rarest birds in the world – is being forced from the last 250 hectares of pristine forest to find food in the village gardens, where it is attacked by domestic cats.

Trouble first came to the islands in 1540 when their discoverer, Juan Fernández, dropped off four goats to provide food for future mariners. Subsequent overgrazing by goats, cattle, sheep, horses and rabbits led to irreversible erosion. Rats and mice also jumped ship to become predators of birds and gnawers of rare plants.

New plants arrived with immigrants and flowers skipped over garden fences to colonise disturbed land and oust vegetation which had evolved over 4 million years. The native magellan thrush unwittingly spreads alien seeds far and wide.

Legend has it that South American coati were released to provide more wildlife interest when the islands were designated a national park in the 1930s only to become predators of the Juan Fernández petrel, a seabird which nests in burrows there and nowhere else. Later, in the 1960s, someone thought the European blackberry would make a good hedge. Now bramble grows into enormous thickets, smothering native trees.

The consensus among conservation scientists is for drastic action: shoot the goats, poison the rats, grub out the bramble. Alan Saunders, who manages New Zealand's invasive species management programme is optimistic: "They say you can't turn the clock back but I say we can get awful close in restoring islands to their previous state. We've eradicated introduced species from New Zealand islands, such as Tiri Tiri Matangi, and we can have a good go with this."

Many in the 600-strong local community on Robinson Crusoe island also back such measures: "We must act now," says one islander, "our islands are dying."